Method for in-situ nondestructive measurement of Young&#39;s modulus of plate structures

ABSTRACT

A method for determining stiffness of a composite laminate plate entails disposing a device for generating an acoustical pulse against a surface of the plate and disposing a detecting device against the same surface spaced a known distance from the pulse-generating device, and using the pulse-generating device to emit a pulse so as to create an extensional wave in the plate. The detecting device is used to determine a time of flight of the wave over the known distance, and the wave velocity is calculated. A Young&#39;s modulus of the plate is determined based on the wave velocity. Methods for both anisotropic and quasi-isotropic laminates are disclosed.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The invention described herein was made in the performance of work underNASA Cooperative Agreement NCC8-39 and is subject to the provisions ofSection 305 of the National Aeronautics and Space Act of 1958 (42 U.S.C.2457).

FIELD OF THE INVENTION

The invention relates to nondestructive test methods for determiningstiffness properties of plate structures. The invention relates moreparticularly to such methods employing propagation of acoustic wavesthrough a plate structure of homogeneous or composite laminate form fordetermining Young's modulus of the plate structure.

BACKGROUND OF THE INVENTION

In a variety of mechanical or structural devices or assemblies, it isfrequently desired to be able to determine changes in materialproperties of a given part, because such changes can be indicative ofdegradation of the part. For example, material stiffness is an importantparameter affecting the performance of a structure. While structures aretypically designed based on a known initial stiffness of the materialsmaking up the structure, various factors can cause the materials to losestiffness. Stress, fatigue, and environmental attack such as thermaland/or oxidation processes are just a few of the mechanisms by which amaterial can be degraded in terms of material stiffnes. Fiber/matrixcomposite materials are particularly susceptible to stiffnessdegradation, chiefly through a process known as micro-cracking in whichmicroscopic cracks develop in the matrix material that binds the fiberstogether. Such micro-cracking can cause deleterious changes inmechanical properties, stress concentration, and redistribution withinthe composite material, which in turn can lead to performancedegradation, delamination, and fiber damage. It is difficult, however,to detect micro-cracking using the types of nondestructive testingmethods that heretofore have been available.

Prior to the present invention, there was no known nondestructivetesting device suitable for use in the field, such as a hand-helddevice, for quantitatively determining changes in stiffness of a platesuch as a composite laminate plate along an in-plane direction of theplate. The prior art teaches various methods for determining stiffnessof isotropic materials using ultrasonic wave propagation through thematerial. For example, U.S. Pat. No. 5,741,971 to Lacy discloses amethod for nondestructively measuring a Young's modulus of a bulkisotropic material, such as cements or completion gels used in thepetroleum industry for interzone isolation and fracture containment indrilling operations. The method involves using the through-transmissiontechnique in which an ultrasonic transducer is disposed adjacent one endof a sample slug of the bulk material and another ultrasonic transduceris disposed adjacent an opposite end of the sample. The length of thesample between the two transducers is known. An ultrasonic pulse isgenerated by one of the transducers so as to cause an ultrasoniccompression or longitudinal wave to be propagated beginning at one endof the sample, and the other transducer detects the wave when it arrivesat the opposite end of the sample. The elapsed time between initiationof the wave at one end of the sample and arrival of the wave at theother end of the sample is measured. Based on this time and the knownlength of the sample, a velocity of the wave through the sample iscalculated. A Young's modulus for the material is then calculated basedon the wave velocity and the known density and Poisson's ratio of thematerial. The method of Lacy and the theory behind it are applicableonly to isotropic materials. Lacy's method requires placing transducerson two opposite sides of the sample, and thus would be difficult toapply to in-situ testing of a structure where it may be difficult orimpossible to access both sides of the structure. Even if both sides ofthe structure could be accessed, the through-transmission technique ofLacy still cannot give a measurement of Young's modulus in an in-planedirection, but can only provide an indication of stiffness in thethickness direction, which is the less interesting of the twodirections.

U.S. Pat. No. 5,154,081 to Thompson et al. discloses a method forultrasonic measurement of material properties for metal plates,involving using two transducers and a receiver arranged non-colinearlyon one side of the plate. The two transducers generate Lamb waves thatpropagate along two different directions to the receiver. Based ondifferences in calculated velocities of the two Lamb waves, Thompsondeduces material properties such as grain orientation and stress. Themethod is applicable only to metals, and does not provide a materialstiffness measurement.

There has been a need, therefore, for a nondestructive method formeasuring in-plane stiffness properties of plates including homogeneousisotropic plates and composite laminate plates. Additionally, there hasbeen a need for such a method that can be used for in-situ examinationof a plate where it may not be possible to access both sides of theplate.

SUMMARY OF THE INVENTION

The above needs are met and other advantages are achieved by the presentinvention, which provides a method for quantitatively evaluatingin-plane stiffness properties of a plate in a nondestructive manner thatis applicable to in-situ use, necessitating access to only one side ofthe plate. The method broadly comprises imparting energy to the plate ata first point located on a first of the major surfaces of the plate soas to cause an elastic wave to originate at the first point andpropagate along the plate as a plate wave or guided wave. The plate wavegenerally consists of two wave modes, i.e., extensional and flexuralwave modes. At a second point on the same surface of the plate andspaced from the first point along an in-plane direction, theextensional-mode wave, which travels faster than the flexural wave, isdetected when it arrives. A velocity of the extensional wave along thein-plane direction of the plate is determined. Based on this velocity, amaterial stiffness of the plate along the in-plane direction iscalculated.

The wave velocity can be determined by measuring the distance d betweenthe first and second points and the elapsed time t required for theextensional-mode wave to travel the distance d from the first point tothe second point, and dividing the distance d by the time t. Based onthe velocity, a stiffness parameter for the plate along the in-planedirection is determined. The determination of the stiffness parameter isbased on elastic wave propagation. The method can be applied to bothhomogeneous isotropic plates and composite laminate plate structures.

In accordance with a preferred embodiment of the invention applicableparticularly to homogeneous isotropic plates, the stiffness parametercalculation in accordance with the invention comprises calculating theYoung's modulus based on the distance d and the time t. Moreparticularly, the Young's modulus E is calculated based on the equation

E=(1−ν²)ρ(d/t)²,

where ν is a predetermined Poisson's ratio for the material of the plateand ρ is a predetermined density of the material of the plate.

Preferably, the elastic wave is generated by applying acoustic energy tothe plate. For example, a device for emitting acoustic pulses can bedisposed against the plate surface and activated to create an acousticpulse. An ultrasonic transducer or acoustic emission sensor can be usedfor this purpose. The extensional wave mode is detected with a secondsensor placed a known distance from the first sensor against the samesurface of the plate. It will thus be appreciated that unlike prior artmethods employing the through-transmission technique in which alongitudinal wave is propagated from one side of a material to theother, the method of the invention is suitable for in-situ applicationswhere it may not be possible or practical to locate sensors on bothsides of the structure.

The methods described above are applicable primarily to isotropic platesand to quasi-isotropic composite laminate plates in which the plies arearranged in a lay-up such that the resulting laminate exhibits isotropicelastic behavior in the plane of the plate. The invention also providesa method for determining Young's moduli of a composite laminate plate inthe more general case of anisotropic laminates. This method involvessolving a set of simultaneous equations to determine Young's moduli forthe plate along two orthogonal in-plane x- and y-directionscorresponding to the zero-degree and 90-degree fiber directions of thelaminate. The equations relate the Young's moduli to the extensionalwave velocities along these directions and to Poisson's ratios andin-plane stiffness parameters for the plate. More specifically, oneembodiment of the invention entails determining extensional wavevelocities C_(x) and C_(y) along the x- and y-directions of a compositelaminate plate, and solving the set of equations:

C _(x)={square root over (A ₁₁ /ρh)}  Eq. (1)

C _(y)={square root over (A ₂₂ /ρh)}  Eq. (2)

$\begin{matrix}{E_{xx} = {\frac{\sigma_{xx}}{\varepsilon_{xx}^{{^\circ}}} = \frac{{A_{11}A_{22}} - A_{12}^{2}}{{hA}_{22}}}} & \text{Eq.~~(3)} \\{v_{xy} = {{- \frac{\varepsilon_{yy}^{{^\circ}}}{\varepsilon_{xx}^{{^\circ}}}} = \frac{A_{12}}{A_{22}}}} & \text{Eq.~~(4)} \\{E_{yy} = \frac{{A_{11}A_{22}} - A_{12}^{2}}{{hA}_{11}}} & \text{Eq.~~(5)} \\{v_{yx} = \frac{A_{12}}{A_{11}}} & \text{Eq.~~(6)}\end{matrix}$

where h is the plate thickness, A_(ij) (i, j=1 and 2) are the in-planestiffnesses of the plate as defined in the composite laminate theory, ρis the plate density, and ν_(xy), and ν_(xy) are Poisson's ratios forthe plate along the x- and y-directions. The plate density and Poisson'sratios will generally be known or can readily be determined. Thus, theseequations can be solved for the Young's moduli. It can be shown, forquasi-isotropic composite plates, that this set of equations can begreatly simplified and reduced to the equation

E=(1−ν²)ρ(d/t)²

set forth above.

The invention also provides a method for quantitatively determining achange in Young's modulus for a plate. The method comprises performing afirst test in which energy is imparted to the plate at a first pointlocated on the plate surface and detecting when the extensional-modewave reaches a second point located on the same surface and spaced apredetermined distance from the first point, and measuring afirst-elapsed time t₁ required for the extensional-mode wave to travelfrom the first point to the second point. A second test is thenperformed in the same manner, making sure that the distance between thetwo points is the same as for the first test. A second elapsed time t₂required for the extensional-mode wave to travel between the two pointsis measured. A change in Young's modulus for the plate is calculatedbased on a degree of difference, of the times t₁ and t₂. Moreparticularly, it is assumed that the density and Poisson's ratio for thematerial of the plate are constant or its change is negligible betweenthe first test and the second test. A ratio of Young's moduli for thefirst and second tests is calculated based on a ratio of the times t₁and t₂. Advantageously, the ratio of Young's moduli is calculated by theequation

E ₂ /E ₁=(t ₁ /t ₂)²,

where E₁ is Young's modulus for the first test and E₂ is Young's modulusfor the second test. The first and second tests may be performed at twodifferent times, in which case the change in Young's modulus representsa change in material stiffness over time. Thus, the method of theinvention can be used for periodic inspection as a way of monitoring thehealth of a structure. The information regarding changes in materialstiffness can be used for prediction of remaining life of the structureor other purposes.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features, and advantages of the inventionwill become more apparent from the following description of certainpreferred embodiments thereof, when taken in conjunction with theaccompanying drawings in which:

FIG. 1 is a schematic depiction of a testing apparatus positioned on aplate structure for measuring a time of flight of an extensional wavealong the plate in accordance with a method of the invention;

FIG. 2 is a flowchart showing a method for determining Young's modulusof a plate structure in accordance with an embodiment of the invention;

FIG. 3 is a flowchart showing a method for determining a change inYoung's modulus of a plate structure in accordance with anotherembodiment of the invention.

DETAILED DESCRIPTION OF THE DRAWINGS

The present invention now will be described more fully hereinafter withreference to the accompanying drawings; in which preferred embodimentsof the invention are shown. This invention may, however be embodied inmany different forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided sothat this disclosure will be thorough and complete, and will fullyconvey the scope of the invention to those skilled in the art. Likenumbers refer to like elements throughout.

The present invention is premised on a unique application of the theoryof extensional wave behavior in plate structures and the compositelaminate theory. It is known from theoretical work on wave behavior incomposite laminate plates that for symmetric and orthotropic laminateplates, the extensional wave velocity in the x-direction (i.e., alongthe 0° ply direction) is given by

C _(x)={square root over (A ₁₁ /ρh)}  Eq. (1)

where A₁₁ is the in-plane stiffness in the x-direction, ρ is the platedensity, and h is the plate thickness. Similarly, the extensional wavevelocity in the y-direction (along the 90° ply direction) is given by

C _(y)={square root over (A ₂₂ /ρh)}  Eq. (2)

where A₂₂ is the in-plane stiffness in the y-direction. By symmetriclaminate is meant a laminate in which the plies are arranged so as to besymmetric about a central plane dividing the plate thickness in half,and in which for every ply of +θ orientation there is an identical plyof −θ orientation. Such a ply lay-up is also commonly referred to as abalanced symmetric ply lay-up.

It is also known that for a balanced symmetric laminate, the Young'smodulus in the x-direction is given by $\begin{matrix}{E_{xx} = {\frac{\sigma_{xx}}{\varepsilon_{xx}^{{^\circ}}} = \frac{{A_{11}A_{22}} - A_{12}^{2}}{{hA}_{22}}}} & \text{Eq.~~(3)}\end{matrix}$

and the Poisson's ratio is given by $\begin{matrix}{v_{xy} = {{- \frac{\varepsilon_{yy}^{{^\circ}}}{\varepsilon_{xx}^{{^\circ}}}} = \frac{A_{12}}{A_{22}}}} & \text{Eq.~~(4)}\end{matrix}$

Similarly, the Young's modulus in the y-direction is $\begin{matrix}{E_{yy} = \frac{{A_{11}A_{22}} - A_{12}^{2}}{{hA}_{11}}} & \text{Eq.~~(5)}\end{matrix}$

and the Poisson's ratio is $\begin{matrix}{v_{yx} = \frac{A_{12}}{A_{11}}} & \text{Eq.~~(6)}\end{matrix}$

The Poisson's ratios ν_(xy) and ν_(yx) are material constants and can bedetermined by mechanical methods or can be calculated from the lamina(single ply) data. Likewise, the density ρ is a material constant andcan readily be determined. Thus, Equations (1) through (6) represent aset of six simultaneous equations having seven unknowns, namely, c_(x),c_(y), A₁₁, A₂₂, A₁₂, E_(xx),and E_(yy). However, consider thesituation, where the extensional velocites c_(x) and c_(y) are known.Then, the equations can be solved to determine the Young's moduli E_(xx)and E_(yy). In other words, the Young's modulus along a defineddirection of a plate can be determined if the extensional wave velocityalong that direction is known.

The extensional velocity along a defined direction of a plate can beexperimentally determined by causing an extensional wave to propagatealong the plate and measuring the time of flight required for the waveto travel a known distance along the plate. The quantitative stiffnessdetermination of the present invention is applicable primarily to thinplates in which the thickness of the plate is much smaller than thelength and width dimensions of the plate. Qualitative results may beobtained, however, even for non-plate structures using the samemethodology as that described herein. It is anticipated thatquantitative results could even be obtained for non-plate structures byusing empirically derived correction factors.

FIG. 1 schematically depicts a testing apparatus that can suitably beused for initiating an extensional wave and measuring a time of flight.A composite laminate plate 10 is schematically depicted as composed of aplurality of plies 12 laid atop one another. FIG. 1 is a view looking atthe plate edgewise. The major surfaces 14 and 16 of the plate define aplate thickness h therebetween. In accordance with a preferredembodiment of the invention, a pair of sensors 18 and 20 are disposedagainst one of the major surfaces of the plate, such as the surface 14as shown. The sensors 18 and 20 each comprises a device for convertingan electrical pulse into an acoustical pulse or signal and vice versa,such as a 50 kHz to 2 MHz ultrasonic transducer or acoustic emissionsensor. The sensor 18 is connected to a suitable processor 22 whichprovides an electrical pulse to the sensor 18 and receives a signal fromthe sensor 18 indicating that an acoustical pulse has been initiated.The processor 22 includes a clock that begins measuring an elapsed timeupon receipt of this signal in a proper sampling rate according to theaccuracy required for the modulus measurements, in a range of above 5MHz. The time required for the extensional wave to travel between thetwo sensors 18 and 20 is equal to the sensor spacing d divided by thesound velocity c. Thus, as an example of determining the proper samplingrate, consider a case in which the sensor spacing d is 0.05 m and thematerial's velocity of sound propagation c is 6000 m/s. Accordingly, toobserve a two percent change in modulus, a minimum sampling rate ofabout 10 MHz would be required. The higher the sampling rate, thesmaller the change in modulus that can be measured.

Upon activation of the sensor 18, an extensional wave will begin to bepropagated through the plate 10. After an elapsed time t measured fromwhen the sensor 18 is activated, the extensional wave will arrive at thelocation of the second sensor 20. Upon, detection of the wave, thesecond sensor 20 sends a signal to the processor 22, and the elapsedtime between initiation of the acoustical pulse at the first sensorlocation and arrival of the extensional wave at the second sensorlocation is determined by the processor 22. The distance d between thesensors 18 and 20 is known. Accordingly, an extensional wave velocitycan be determined by dividing the distance d by the elapsed time t.

The wave velocity determined in this manner is the velocity along aparticular direction of the plate 10 defined by the orientation of thesensors 18, 20 with respect to each other. In the general case of ananisotropic composite laminate, the in-plane stiffnesses A₁₁ and A₂₂ inthe x- and y-directions are different, and thus the extensional wavevelocities are different in different directions, as indicated byEquations (1) and (2) above. Examination of Equations (3) and (5) alsoreveals that the Young's moduli are different in the x- andy-directions. The present invention provides a method for determiningthe Young's moduli along the x- and y-directions by measuring theextensional wave velocities along these directions, and using themeasured velocities in the above Equations (1) to (6) to deduce theYoung's moduli. This method is applicable to the general case of ananisotropic laminate. It should be noted that the x and y axisdirections coincide with the zero-degree and 90-degree fiber directionsof the laminate, respectively. Such a coordinate system gives thesimplest form of equations for the Young's modulus measurements thatpractically are most convenient for engineering evaluation. Thus, itwill be understood that in order to evaluate the modulus of a platealong the x-axis direction using the equations given above, the sensorsmust be aligned along the direction corresponding to the zero-degreefiber direction.

In many composite structures, however, quasi-isotropic ply lay-ups areused because of their advantageous properties. For a quasi-isotropiclaminate, the in-plane stiffnesses A₁₁ and A₂₂ are equal. Accordingly,Equations (1) and (2) indicate that the extensional velocities in the x-and y-directions will be equal and can be denoted simply as c_(e).Similarly, Equations (4) and (6) indicate that the Poisson's ratiosν_(xy) and ν_(yx) will be equal and can be denoted simply as ν. Thein-plane stiffness A₁₁ can be expressed in terms of the extensionalvelocity c_(e) by rearranging Equation (1), and the term A₂₂ in all ofthe equations can be replaced by A₁₁. From Equation (4), A₁₂ can beexpressed in terms of A₁₁ and Poisson's ratio ν. Making the appropriatesubstitutions, Equations (3) and (5) both reduce to the same equation,

E=(1−ν²)ρc _(e) ²  (7)

Thus, the Young's moduli along the x- or y-directions are equal and canbe determined by measuring the wave velocity along either direction andusing Equation (7). Thus, in the case of quasi-isotropic compositelaminates, a simplified method can be used to deduce stiffnessnecessitating only a single measurement of wave velocity along anydirection in the plane.

FIG. 2 is a flowchart illustrating a method in accordance with oneembodiment of the invention applicable particularly to homogeneousisotropic or quasi-isotropic composite laminate plates. As indicated at30, suitable acoustic devices such as contact ultrasonic transducers oracoustic emission sensors are placed against the same surface of a plateto be tested such that the sensors are a known distance d apart and areappropriately aligned relative to the fiber directions of the laminate.One of the sensors is activated to emit an acoustical pulse or signal toinitiate a plate wave, and the other sensor detects the arrival of theextensional-mode wave component of the plate wave (which travels fasterthan the flexural-mode component and thus is the first to arrive at thesensor). From the sensor information, a time of flight t is measured asindicated at 40. Then, at 50, the Young's modulus E for the plate iscalculated based on Equation (7) above, where the wave velocity c_(e) isequal to d/t.

This method can be further simplified for applications where repeatedmeasurements of the time of flight t are made on a periodic basis, forexample, as part of a regular health-monitoring inspection program. Inthis case, it may be desired only to determine a quantitative change inYoung's modulus from one inspection or time to another. If Equation (7)is expressed in terms of time of flight t by substituting d/t for thewave velocity c_(e), a Young's modulus for an i-th measurement is givenby $\begin{matrix}{E_{i} = {\left( {1 - v^{2}} \right){\rho \left( \frac{d}{t_{i}} \right)}^{2}}} & (8)\end{matrix}$

Consider that at some earlier measurement, an original Young's moduluswould have been given by $\begin{matrix}{E_{o} = {\left( {1 - v^{2}} \right){\rho \left( \frac{d}{t_{o}} \right)}^{2}}} & (9)\end{matrix}$

Next, it is assumed that for each inspection, the sensors are,placed thesame distance d apart from each other along the same direction. It isfurther assumed that the density and Poisson's ratio do not change fromone inspection to the next. This assumption is considered to be close toreality, inasmuch as the type of material changes of most interest incomposite laminates are micro-cracking and other microscopic damage, andthus the changes in Poisson's ratio should be negligible. Accordingly,the ratio of Young's modulus at the i-th measurement to the originalYoung's modulus, is given by $\begin{matrix}{\frac{E_{i}}{E_{o}} = \left( \frac{t_{o}}{t_{i}} \right)^{2}} & (10)\end{matrix}$

This can also be expressed in terms of a fractional change as$\begin{matrix}{\frac{\Delta \quad E}{E_{o}} = {1 - \left( \frac{t_{o}}{t_{i}} \right)^{2}}} & (11)\end{matrix}$

FIG. 3 is a flowchart illustrating a testing sequence based on theEquations (10) and (11). As indicated at 60, sensors are placed on theplate surface a distance d apart from each other along a predetermineddirection. At 70, the time of flight t₁ of an extensional wave ismeasured with the sensors. The test is repeated as indicated at 80,making sure that the sensors are placed the same distance d apart alongthe same direction as for the prior test, so as to measure a second timeof flight t₂. At 90, the change in Young's modulus is calculated usingeither Equation (10) or (11), or both, based on the ratio of the twotimes of flight.

From the foregoing, it will be appreciated that the invention provides amethod for nondestructively determining quantitative stiffnessinformation for homogeneous and composite laminate plate structuresusing extensional wave propagation. The method is readily applicable toin-situ inspection because sensors are placed on the same surface of thestructure being tested, and therefore it is not necessary to have accessto both sides of the plate structure. The sensors advantageously can bepermanently bonded on a structure in a critical location for frequentinspection, thereby facilitating testing and also assuring that thesensor spacing and orientation are always fixed in the appropriatemanner.

Many modifications and other embodiments of the invention will come tomind to one skilled in the art to which this invention pertain's havingthe benefit of the teachings presented in the foregoing descriptions andthe associated drawings. For example, although the foregoing descriptionfocuses primarily upon the unique problems associated with evaluatingcomposite laminate plates, the method of the invention is equallyapplicable to homogeneous isotropic plates, as will be recognized bythose skilled in the art. Therefore, it is to be understood that theinvention is not to be limited to the specific embodiments disclosed andthat modifications and other embodiments are intended to be includedwithin the scope of the appended claims. Although specific terms areemployed herein, they are used in a generic and descriptive sense onlyand not for purposes of limitation.

What is claimed is:
 1. A nondestructive method for quantitativelyevaluating a material stiffness of a composite laminate plate along anin-plane direction, the plate having a plurality of plies arranged in abalanced symmetric ply lay-up and having opposite major surfacesdefining a thickness of the plate therebetween, the method comprising:propagating an elastic extensional-mode wave through the plate alongsaid in-plane direction; determining a velocity of the extensional-modewave along said in-plane direction of the plate; and calculating amaterial stiffness of the plate along said in-plane direction based onthe wave velocity.
 2. The method of claim 1, wherein propagating theextensional-mode wave comprises: imparting energy to the plate at afirst point located on a first of the major surfaces of the plate so asto cause the extensional-mode wave to originate at said first point andpropagate along the plate.
 3. The method of claim 2, wherein determiningthe wave velocity comprises: detecting when the extensional-mode wavereaches a second point located on said first major surface and spaced insaid in-plane direction from the first point; determining a distance dbetween the first and second points along said first major surface ofthe plane in said in-plane direction; measuring an elapsed time trequired for the extensional-mode wave to travel the distance d from thefirst point to the second point; and calculating the wave velocity basedon the distance d and the time t.
 4. The method of claim 3, whereincalculating the material stiffness comprises calculating a Young'smodulus along said in-plane direction.
 5. The method of claim 4, adaptedfor evaluating a quasi-isotropic composite laminate plate, wherein theYoung's modulus E is calculated based on the equation E=(1−ν²)ρ(d/t)²,where ν is a predetermined Poisson's ratio for the material of the plateand ρ is a predetermined density of the material of the plate.
 6. Themethod of claim 3, wherein detecting when the extensional-mode wavereaches the second point comprises using an acoustic energy detectordisposed against the first major surface of the plate at the secondpoint.
 7. The method of claim 2, wherein imparting energy to the platecomprises using acoustic energy to create the extensional-mode wave. 8.The method of claim 2, wherein imparting energy to the plate comprisesdisposing a device for emitting acoustical energy against the firstmajor surface of the plate at the first point and activating the deviceto emit acoustic energy.
 9. A nondestructive method for quantitativelyevaluating Young's moduli of a composite laminate plate along twoorthogonal in-plane x- and y-directions of the plate, comprising:propagating an extensional wave through the plate; determining avelocity c_(x) of the extensional wave along said x-direction;determining a velocity c_(y) of the extensional wave along saidy-direction; determining Young's moduli E_(xx) and E_(yy) respectivelyalong the x- and y-directions by solving a set of simultaneous equationsrelating the extensional wave velocities, the Young's moduli, andPoisson's ratios and in-plane stiffness parameters for the plate to oneanother.
 10. The method of claim 9, wherein the Young's moduli E_(xx)and E_(yy) are determined by solving the set of equations: C_(x)={square root over (A ₁₁ /ρh)}  C _(y)={square root over (A ₂₂ /ρh)}$E_{xx} = {\frac{\sigma_{xx}}{\varepsilon_{xx}^{{^\circ}}} = \frac{{A_{11}A_{22}} - A_{12}^{2}}{{hA}_{22}}}$$v_{xy} = {{- \frac{\varepsilon_{yy}^{{^\circ}}}{\varepsilon_{xx}^{{^\circ}}}} = \frac{A_{12}}{A_{22}}}$$E_{yy} = \frac{{A_{11}A_{22}} - A_{12}^{2}}{{hA}_{11}}$$v_{yx} = \frac{A_{12}}{A_{11}}$

where h is a thickness of the plate, ρ is a known density of the plate,and ν_(xy) and ν_(yx) are known Poisson's ratios for the plate.
 11. Anondestructive method for quantitatively evaluating a change in Young'smodulus of a composite laminate plate along an in-plane direction, theplate having a plurality of plies arranged in a balanced symmetric plylay-up and having opposite major surfaces defining a thickness of theplate therebetween, the method comprising: (1) performing a first testincluding steps (a) through (c) comprising: (a) imparting energy to theplate at a first point located on a first of the major surfaces of theplate so as to cause an extensional-mode wave to originate at said firstpoint and propagate along the plate in said in-plane direction; (b)detecting when the extensional-mode wave reaches a second point locatedon said first major surface and spaced a predetermined distance in saidin-plane direction from the first point; and (c) measuring a firstelapsed time t₁ required for the extensional-mode wave to travel fromthe first point to the second point; (2) performing a second testincluding steps (d) through (f) comprising: (d) imparting energy to theplate at a third point located on a first of the major surfaces of theplate so as to cause an extensional-mode wave to originate at said thirdpoint and propagate along the plate in said in-plane direction; (e)detecting when the extensional-mode wave reaches a fourth point locatedon said first major surface and spaced from the third point by the samesaid predetermined distance along said in-plane direction; and (f)measuring a second elapsed time t₂ required for the extensional-modewave to travel from the third point to the fourth point; and (3)calculating a change in Young's modulus for the plate along saidin-plane direction based on a degree of difference of the times t₁ andt₂.
 12. The method of claim 11, wherein the first and second tests areperformed at two different times, whereby the change in Young's modulusrepresents a change over time.
 13. The method of claim 11, wherein thecalculation of change in Young's modulus is based on an assumption thatdensity and Poisson's ratio for the material of the plate are constantbetween the first test and the second test.
 14. The method of claim 11,wherein calculating the change in Young's modulus comprises calculatinga ratio of Young's moduli for the first and second tests based on aratio of the times t₁ and t₂.
 15. The method of claim 14, wherein theratio of Young's moduli is calculated by the equation E ₂ /E ₁=(t ₁ /t₂)², where E₁ is Young's modulus for the first test and E₂ is Young'smodulus for the second test.
 16. A method for quantitatively evaluatinga material stiffness of an isotropic or quasi-isotropic plate along anin-plane direction, the method comprising: disposing a first device foremitting acoustical energy on a first major surface of the plate andactivating the device to cause an elastic extensional-mode wave to bepropagated through the plate along said in-plane direction; disposing asecond device for detecting the extensional-mode wave on said firstmajor surface of the plate spaced a distance d from the first devicealong said in-plane direction and using the second device to detectarrival of the extensional-mode wave; measuring the elapsed time tbetween initiation of the extensional-mode wave by the first device anddetection of the extensional-mode wave by the second device; andcalculating Young's modulus E of the plate along said in plane directionbased on the equation E=(1−ν²)ρ(d/t)², where ρ is a predetermineddensity of the plate and ν is a predetermined Poisson's ratio of theplate along said in-plane direction.
 17. The method of claim 16, furthercomprising permanently bonding the first and second devices to saidfirst major surface of the plate, and periodically performing tests withthe devices to determine Young's modulus at a plurality of sequentialtimes, whereby the spacing between the devices and the devices'orientation relative to the plate are assured to be fixed from one testto another.